Textbook Question
Rewrite each statement with > so that it uses < instead. Rewrite each statement with < so that it uses >. See Example 6. 6 > 2
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Ch. R - Algebra Review
Lial12th EditionTrigonometryISBN: 9780136552161
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Table of contents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Chapter 1, Problem 73
Simplify each complex fraction. See Examples 5 and 6. (5/8 + 2/3) ÷ (7/1 − 1/4)
Verified step by step guidance1
Identify the complex fraction as a division of two fractions: the numerator is \(\frac{5}{8} + \frac{2}{3}\) and the denominator is \(\frac{7}{3} - \frac{1}{4}\).
Find a common denominator for the fractions in the numerator to combine them: for \(\frac{5}{8}\) and \(\frac{2}{3}\), the common denominator is 24. Rewrite each fraction with denominator 24 and add them.
Similarly, find a common denominator for the fractions in the denominator: for \(\frac{7}{3}\) and \(\frac{1}{4}\), the common denominator is 12. Rewrite each fraction with denominator 12 and subtract them.
After simplifying both the numerator and denominator to single fractions, rewrite the complex fraction as a division of two fractions: \(\frac{\text{numerator fraction}}{\text{denominator fraction}}\).
Recall that dividing by a fraction is the same as multiplying by its reciprocal. Multiply the numerator fraction by the reciprocal of the denominator fraction and simplify the resulting fraction if possible.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Complex Fractions
A complex fraction is a fraction where the numerator, denominator, or both contain fractions themselves. Simplifying involves rewriting the complex fraction as a single simple fraction by performing operations on the numerator and denominator separately before dividing.
Recommended video:
4:22
Dividing Complex Numbers
Addition and Subtraction of Fractions
To add or subtract fractions, they must have a common denominator. Find the least common denominator (LCD), convert each fraction accordingly, then add or subtract the numerators while keeping the denominator the same.
Recommended video:
4:02Solving Linear Equations with Fractions
Division of Fractions
Dividing by a fraction is equivalent to multiplying by its reciprocal. After simplifying the numerator and denominator of a complex fraction, divide by multiplying the numerator by the reciprocal of the denominator to get the final simplified fraction.
Recommended video:
4:02Solving Linear Equations with Fractions
Related Practice
Textbook Question
Simplify each radical. See Example 5. √75
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Textbook Question
Graph each function. See Examples 6–8. ƒ(x) = √x + 2
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Textbook Question
Graph each function. See Examples 6–8. ƒ(x) = √-x
Textbook Question
Use a number line to determine whether each statement is true or false. -3 > -3
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Textbook Question
Simplify each complex fraction. See Examples 5 and 6. [ (−4/3) + 12/5 ] / [ 1 − (−4/3)(12/5) ]
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